Consider the formula for the interest rate gap:

GapGap$==$Amount$$of$$IR$-$sensitive$$Assets$$Amount$$of$$IR$-$sensitive$$LiabilitiesAmount$$of$$IR$-$sensitive$$Assets$$Amount$$of$$IR$-$sensitive$$Liabilities

Banks would like to have a positive gap if they expect that future interest rates will$.$ This means that banks should hold$$interest rate$$sensitive assets than interest rate$$sensitive liabilities.

Now consider the formula for the duration gap:

Duration$$gapDuration$$gap$==$Asset$$Duration$$Liability$$Duration$$LiabilityAssetAsset$$Duration$$Liability$$Duration$$LiabilityAsset

where AssetAsset$$is the market value of the asset, Liability$$Liability$$is the market value of the liability, and durationduration$$is the weighted average of times until payment, with their weights proportionate to the present value of the payment: Duration$=$t$=1$n$($t$$Paymentt$(1+$r$)$t$)$t$=1$nPaymentt$(1+$r$)$tDuration$=$t$=1$nt$$Paymentt$1+$rt$$t$=1$nPaymentt$1+$rt$.$

The duration formula$$implies that if interest rates decrease, duration will$.$ The duration gap formula$$implies that, ceteris paribus, the gap will increase, if the interest rate change affects the value of the bank's assets$$than it affects the value of its liabilities.